MinT - Best Known (157, 157+65, s)-Nets in Base 4

Best Known (157, 157+65, s)-Nets in Base 4

(157, 157+65, 531)-Net over F₄ — Constructive and digital

Digital (157, 222, 531)-net over F₄, using

3 times m-reduction [i] based on digital (157, 225, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 75, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(157, 157+65, 1003)-Net over F₄ — Digital

Digital (157, 222, 1003)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+65, 61312)-Net in Base 4 — Upper bound on s

There is no (157, 222, 61313)-net in base 4, because

1 times m-reduction [i] would yield (157, 221, 61313)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 358456 541427 749719 988234 146004 617029 033621 978336 760546 239992 780562 593395 968918 641158 590464 343257 752104 072710 472295 800369 939240 735140 > 4²²¹ [i]